When the islamist movement known as Hamas first took control of Gaza in 2006, the family of Ahmed Ayyash, a third-year engineering student at the Hamas-controlled Islamic University, gave the party their full backing. Like a solid plurality of Palestinian voters, they thought the Islamists would provide clean government, in contrast to the corruption-riddled Fatah that had ruled for years. Then Ayyash's mother applied for a teaching job. She was offered it immediately: to the Hamas official who interviewed her, all that mattered was that her husband knew people in the new government. A principled woman, Ayyash's mother turned down the job because, he says, "it was through wasta." That's Arabic for connections, and in Gaza it symbolized everything that was wrong with the old administration, everything Hamas claimed to oppose. "This was their slogan at election time, to end the wasta," Ayyash recalls.

Ayyash lost faith in the Islamists early, and in the six years since, he's been joined by many other Gazans who complain that Hamas' patronage politics favors the few while the majority suffer. "Some homes have four or five family members working, and some have none. That's not fair," says Safaa Abu Elaish, 23, an engineer who has been unable to find a job since getting a degree at Islamic University this year. Those who have jobs have other complaints. Ansaf-Bash Bash, 66, a receptionist at the same university, says she's spent eight years on the waiting list for a government-sponsored pilgrimage flight to Mecca. "Some people go almost every year," she says. "If you know someone strong, they forward your name." (See pictures of life under Hamas in Gaza.)

Such complaints, damaging to any political party, are potentially fatal to the Islamists. Besieged by Israel and the West, which regards it as a terrorist group, and cut off from the Palestinian majority in the West Bank, Hamas has little to offer beyond its jihadist credentials  and the promise of clean government. So it's hardly surprising that the party has been rapidly losing ground in its stronghold. Recent surveys by leading pollsters conclude that if elections were held in Gaza today, Hamas, an acronym in Arabic for the Islamic Resistance Movement, would not be returned to power. A June poll by the Palestinian Center for Policy and Survey Research found that Hamas would get just 28% of the vote, a steep decline from the 44% plurality it won in 2006.

Especially alarming for the Islamists is a precipitous drop in support for the party among Gaza's youth: two-thirds of the population is under 25. In a March survey taken in the afterglow of the protests in Cairo's Tahrir Square that led to the ouster of Egypt's dictator, Hosni Mubarak, more than 60% of Gazans age 18 to 27 said they too would support public demonstrations demanding regime change.

Soon after that poll, 10,000 turned out at a rally to voice a more modest demand  that Hamas end the bloody rift with Fatah, the secular party it bested six years ago. Hamas sent thugs to break up the demonstration. "We came out to say the people should be united, and they attack us!" says Shadi Hassan, 22, who lives in a refugee camp and sells cigarettes. "We are suffocated, and we need regime change." (See a TIME photoessay on Hamas Recruitment Day.)

The rally was not in vain: Hamas and Fatah promptly announced they were reconciling. Their pact promises new elections by next May, but the Islamists may not be looking forward to the vote. Hamas will need something dramatic to regain the Gaza street. It may get a short-term boost from its surprise deal to release Israeli soldier Gilad Shalit, held hostage since the summer of 2006, in exchange for more than 1,000 Palestinians imprisoned by Israel. But the euphoria over the release is unlikely to alleviate the bread-and-butter problems for which many Gazans blame the party.